This paper explores the relationship between longevity risk and health status transition under the framework of life cycle model to explore the optimal insurance allocation including annuity and nursing insurance under different incidence scenarios and the old-age security needs of residents Based on the data from China Health and Pension Tracking Survey (CHARLS), this paper calculates the health state transition probability of residents and calibrates the health state transition probability by using the mortality data of Lee-Carter model, and then solves the optimal insurance decision of residents under different incidence scenarios by multi-period life cycle model The results show that the demand for first annuity and nursing insurance is influenced by initial endowment, health status, minimum living and bequest motivation Residents with lower initial endowments are reluctant to buy annuities and nursing insurance because of precautionary savings motivation Expenditure on care insurance when purchasing both annuities and care insurance may weaken the demand for annuities Secondly, under the interaction of longevity risk and health status transition, residents have higher disability probability and higher demand for annuity and nursing insurance under the scenario of expanding incidence Thirdly, under the optimal wealth decision, the optimal allocation of annuity and nursing insurance makes the wealth level of residents more stable

According to the theory of unit root test, Lee-Carter model and generalized linear model, which are widely used in mortality projection, impose key implicit assumptions respectively which are inconsistent with each other. Log mortality rate (the force of mortality or the central mortality rate) is described as a unit root process in Lee-Carter model, while it is modeled as a deterministic trend process in generalized linear model. We use panel LM unit-root tests with level shifts to test the assumptions in above models, based on mortality data of the 7 most developed countries(G7) and Nordic countries(Denmark, Finland, Norway, Sweden). The test results show that a mortality projection model, whatever it is Lee-Carter model or generalized linear model, is not always appropriate to predict dynamic mortality rates of different countries. Further, we explain period effect and cohort effect of dynamic mortality according to the results of structural break test. Based on the empirical results, we extend Lee-Carter model, which includes a special case of generalized linear model. To check the performance of the extended model, we use it to forecast USA and Sweden mortality and we find that the extended Lee-Carter model works better than the original Lee-Carter model.